Revision of linear simultaneous equations - making the graphical and algebraic links explicit
It's been a while since I last did a Pick of Twitter, which is personally quite annoying because it's my only way of chronicling all the good stuff I see on there - I'm going to try and get back into the habit on Sundays from now on!
Just a quick post today with a few useful goodies for the new Maths GCSE - these are all links I've found useful in planning and resourcing our schemes of work.
I've written quite a few posts recently about using ratio tables extensively in my teaching for proportional reasoning. Following the explosion on Twitter about Edexcel's non-calculator paper last Thursday, I thought it might be time for a critical evaluation on my part of just how useful (or not!) they are in tackling any or all of the proportional reasoning problems on the most recent paper, particularly if we should see this as an indicator of things to come, as @El_Timbre suggested in this brilliant blog post on Sunday.
I'm approaching this from the point of view of pupils aiming for a grade C, as I've had borderline groups for the last two years, and no top GCSE sets for about four, due to having plenty of A Level Maths on my timetable already, so I'll admit that my pedagogy and knowledge of grade A/A* topics at GCSE is fairly limited.
I started writing about multiplication methods yesterday (read Part 1 here), but waffled for rather longer than necessary, and as a result, didn't actually get to discuss what I originally wanted to, namely which from grid, lattice (Gelosia, Chinese, Napier's etc) or long multiplication we should be teaching as a method to pupils.
In one of those weird twists of coincidence, I went on some subject leader training today run by Sheila Eastwood, and we ended up discussing - you guessed it - exactly what I blogged about yesterday, and how this fits in with the idea of mastery in mathematics. We pretty much concluded as I did yesterday; at the moment, no-one really knows what will be allowable as a method on the new GCSE papers.
So in my follow-up post, I thought I'd look at pros and cons of all three methods on the assumption that pupils are allowed to use any in the new GCSE exams, and then consider implications for only allowing long multiplication at the end. Any claims I'm making here are backed up by absolutely no proper research and are mostly anecdotes from my classroom, but I can't seem to find much independent research on multiplication methods.
As a department, we seem to have spent the last six months debating exactly which method is OK for multiplying large numbers. Personally, I learnt column/long multiplication at school, and got pretty good at it, although to be honest, past about midway through Year 11 I can't recall a situation where I've really had to accurately multiply two large numbers without a calculator - but that's another debate. Teacher training introduced me to the grid method, and I immediately went "ooh fantastic!" and taught that for three years without any critical thought as to whether or not that's even the best method.
Then I did this activity from the NCETM and several of my Year 7s decided they really liked Gelosia multiplication. Some of them had previously been really unsuccessful with grid method - although they understood what they were doing, they invariably lost the odd zero along the way, or made a pig's ear of lining up the addition calculation at the end. I told them to go with Gelosia if they understood it.
Excuse the pun, I'm just quite excited about the Celebration of Maths event tomorrow. Due to the fact that I'm going to the bar modelling session tomorrow (and that I'm a geek who loves doing Maths on a Friday night), I decided to go on a bar modelling hunt using the Foundation paper 1 from the Edexcel GCSE 9-1 Sample Assessment materials.
As a side note, this is the first time I've sat down and properly worked through any of the new SAMs... and man, they are hard! It will be interesting to see what comes out of the Ofqual stuff in the next few months. But regardless, I've gone through and picked out all the questions that (I think) could be done using bar modelling. The last hour has made me re-evaluate my ideas about bar modelling as the absolute best thing that's happening in maths teaching - don't get me wrong, I'm loving it for developing understanding while teaching new concepts, particularly for fractions and ratio, but I'm more convinced that there's still a place for "standard methods" than I was six months ago.
Anyway, here are some mathematical scribblings and ramblings. Due to copyrighting etc, I'm not reproducing any of the original materials on here, so you might want to open a copy of the paper too.